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POST UTME REDEEMERS UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side using the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 14 cm

D. 16 cm

Correct Answer: B

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Question 2 View Details

A random variable X has a probability distribution given by (P(X) = \begin{cases} 0.2 & \text{if}\(X = 1\)\\((P(X) = begin{cases} 0.2 & \ 0.3 & \text{if} X = 2 \\\( 0.3 & text{if} X = 2 \ 0.5 & \text{if} X = 3 \end{cases}\). Find the expected value of X.

Correct A. 1.4

B. 1.7

C. 2.1

D. 2.5

Correct Answer: A

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Question 3 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\).

A. -2

Correct B. -3

C. -1

D. 4

Correct Answer: B

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Question 4 View Details

A histogram of exam scores is given below. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 5 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & 2 \\ 3 & 2 & 1 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 2x\) about the x-axis.

Correct A. \(\frac{4}{3}\)\)\pi

B. \(\frac{2}{3}\)\)\pi

C. \(\frac{1}{3}\)\)\pi

D. \(\frac{1}{2}\)\)\pi

Correct Answer: A

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Question 7 View Details

A random variable X has a probability distribution given by \(P X = k\) = \(\frac{1}{2^k}\)\)\)\) for \(k = 1, 2, 3, \dots\). Find the expected value of X.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8 View Details

In the diagram below, (ABCD\) is a trapezium with \(AB = 6\\((ABCD) is a trapezium with\) cm and (CD = 8\) cm. If \(E\\((CD = 8) cm. If\) is the midpoint of (BC\), find the area of the triangle \(ADE\\((BC), find the area of the triangle\).

A. 12

Correct B. 15

C. 18

D. 20

Correct Answer: B

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Question 9 View Details

A quadratic equation has roots \(\alpha\) and \(\beta\) such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\). Find the equation of the quadratic.

Correct A. \\((x^2 - 3x + 2\)\(= 0\)\)

B. \\((x^2 - 3x - 2\)\(= 0\)\)

C. \\((x^2 + 3x + 2\)\(= 0\)\)

D. \\((x^2 + 3x - 2\)\(= 0\)\)

Correct Answer: A

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Question 10 View Details

A histogram of the heights of students in a class is shown below. If the total number of students is 50, find the mean height of the students.

A. 160

B. 170

Correct C. 180

D. 190

Correct Answer: C

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Question 11 View Details

Find the area under the curve of \(y = \frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).

Correct A. 0.7854

B. 0.4636

C. 0.5723

D. 0.6931

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 13 View Details

Find the determinant of the matrix \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14 View Details

A sequence is defined by \(a_n = 2n + 1\). Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 15 View Details

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24

Correct B. 62.83

C. 78.54

D. 100.53

Correct Answer: B

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Question 16 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5) in the coordinate plane.

A. \(y = 2x - 1\)

Correct B. \(y = 2x + 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: B

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() > 0.\)

Correct A. \(-3, -1\) \cup (1, 3)

B. \(-3, -1\) \cup (1, 3) \cup (3, 4)

C. \(-3, -1\) \cup (1, 3) \cup \(-4, -3\)

D. \(-3, -1\) \cup (1, 3) \cup \(-4, -3\) \cup (3, 4)

Correct Answer: A

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Question 18 View Details

Find the probability that the sum of the numbers on the faces of two fair six-sided dice is 7.

A. \(\frac{1}{6}\)\)

B. \(\frac{1}{12}\)\)

C. \(\frac{1}{36}\)\)

Correct D. \(\frac{5}{36}\)\)

Correct Answer: D

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Question 19 View Details

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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Question 20 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.

Correct A. \{(2, 2)\}

B. \{(2, 3)\}

C. \{(3, 1)\}

D. \{(4, 0)\}

Correct Answer: A

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Question 21 View Details

Determine the value of \(\int_0^\pi \frac{\sin^2 x}{1 + \cos^2 x} dx\).

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

C. \(\frac{\pi}{8}\)\)

D. \(\frac{\pi}{16}\)\)

Correct Answer: A

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Question 22 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(-\infty, -1\) \cup \(4, \infty\)

B. \(-\infty, -1\) \cup \(1, \infty\)

C. \(-\infty, 1\) \cup \(4, \infty\)

D. \(-\infty, 1\) \cup \(2, \infty\)

Correct Answer: A

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Question 23 View Details

Find the equation of the line passing through the points \(-2, 3\)\) and \(1, -2\)\).

Correct A. \(y = -\)\(\frac{5}{3}\)\) x + \(\frac{13}{3}\)\)

B. \(y =\)\(\frac{5}{3}\)\) x - \(\frac{13}{3}\)\)

C. \(y = -\)\(\frac{3}{5}\)\) x + \(\frac{13}{5}\)\)

D. \(y =\)\(\frac{3}{5}\)\) x - \(\frac{13}{5}\)\)

Correct Answer: A

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Question 24 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. \(\frac{1}{2}\)\)

B. \(\frac{1}{4}\)\)

C. \(\frac{3}{4}\)\)

D. \(\frac{3}{5}\)\)

Correct Answer: A

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Question 25 View Details

Find the magnitude of the vector \(\vec{a} = \langle 3, 4 \rangle\).

A. 5

Correct B. \(\sqrt{5}\)

C. \(\sqrt{10}\)

D. \(\sqrt{20}\)

Correct Answer: B

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